x^{''}+4x=289+e^t*sin(2t)

Lösung

x^{^{''}} + 4 x = 289 + e^{t} \cdot sin (2 t)

x = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{289}{4} + \frac{e ^{t} sin ( 2 t ) - 4 e ^{t} cos ( 2 t )}{17}

Schritte zur Lösung

x^{''} (t) + 4 x = 289 + e^{t} \cdot sin (2 t)

Solve linear ODE:

x = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{289}{4} + \frac{e ^{t} sin ( 2 t ) - 4 e ^{t} cos ( 2 t )}{17}

x = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{289}{4} + \frac{e ^{t} sin ( 2 t ) - 4 e ^{t} cos ( 2 t )}{17}

\frac{d ^{2} y}{d x ^{2}} + y = 2 x sin (x)

2 y^{^{''}} + 3 y^{^{'}} - 2 y = 10 x^{2} - 8 x - 15

y^{^{''}} + 49 y = - 5 cos (7 t + \frac{π}{3}), y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 6 y^{^{'}} + 13 y = x^{2}

y^{^{''}} + 9 y = 6 cos (3 x) + 9 sin (3 x)